1. Field of the Invention
The present invention relates to the field of the simulation of signal responses of nonlinear amplifiers. An object of the invention is a system for the simulation of the response signal of a nonlinear amplifier having a memory effect.
A system of this kind can be applied to the simulation of high efficiency microwave amplification, especially in the AB, B or C class of amplification and more particularly to the simulation of the response of solid state power amplifiers (SSPA) and travelling wave tube amplifiers (TWT) used in land or satellite transmission radio links.
At high frequencies or at high efficiency, amplifier devices of this kind have a nonlinear characteristic response curve.
2. Description of the Prior Art
FIG. 1 illustrates an exemplary input/output response curve of a nonlinear amplifier ANL. The curve giving the output signal level g of the amplifier ANL as a function of the input signal level x is typically inflected at the high amplitudes A of the input signal x because of saturation phenomena. When the amplifier is used in conditions such that the gain is not constant as a function of the input signal level x, it is said to be an amplifier working in nonlinear mode or more simply the amplification is called nonlinear amplification.
Nonlinear devices can be divided into memoryless devices, quasi-memoryless devices and devices with memory.
Memoryless amplifiers have high nonlinearity in amplitude and a lower phase distortion. The input/output response characteristic of a memoryless nonlinear amplifier ANL can then be reduced, as shown in FIG. 1, to a single curve g(x).
It is possible to model and simulate the response, as a function of the time t, of an memoryless amplifier ANL to a sinusoidal input signal x, with a frequency f.sub.0, that is amplitude modulated A and phase modulated .phi., the signal having the following form: EQU x(t)=A(t).cos(2.f.sub.0.t+.phi.(t)) (1)
A(t) represents the envelope of the input signal, which is defined by the amplitude limits in which the sine signal x evolves, the envelope varying as a function of time. FIG. 3 illustrates a timing diagram of a signal x(t) having a constant envelope A.
The output signal g of the memoryless amplifier then has the following form: EQU g(t)=C(A(t)).cos(2.pi..f.sub.0.t+.phi.(t)) (2)
It is useful to give a complex envelope to these signals x and g in abandoning any reference to the time t since the memoryless amplifiers have an instantaneous response.
The input signal x of the equation (1) has a complex envelope X with the following form: EQU X=A.exp(j..phi.) (3)
All the useful information pertaining to the amplitude modulation A(t) and phase modulation .phi.(t) is recorded in this complex envelope X.
The output signal g of equation (2) similarly has a complex envelope G with the following form: EQU G=C(A).exp(j..phi.) (4)
For a memoryless nonlinear amplifier ANL, it is shown that C(A) is the Chebyshev transform of the input/output response curve g(x).
The response of a :memoryless nonlinear amplifier ANL to a modulated signal x can therefore be modeled and simulated simply by a single curve C(A), whose example is shown in an unbroken line in FIG. 6A. A curve of this kind giving the output amplitude C as a function of the input amplitude A is called a curve of nonlinearity in amplitude and is referenced in abbreviated form as an AM/AM curve.
FIG. 2 illustrates a response characteristic of a nonlinear amplifier with memory ANLAM on which there appears a phenomenon of hysteresis prompted by a memorizing effect. It can be seen that the rising hysteresis curves m and m' are not superimposed on each other when the respective amplitudes A and A' of the input signal x are different. The variation in memorizing time related to the variation in amplitude prevents the curves m and m' from getting superimposed on each other.
When the memorizing time of the amplifier ANLAM is negligible in comparison to the period of the amplitude variation A(t), it can furthermore be considered that the amplitude A is stable and the amplifier is called a quasi-memoryless amplifier.
FIG. 4 shows a timing diagram of an output signal y of a quasi-memoryless amplifier to which there is applied the input signal x illustrated by the timing diagram of FIG. 3 whose formula is recalled here below: EQU x(t)=A(t).cos(2.pi..f.sub.0.t+.phi.(t)) (1)
For a quasi-memoryless nonlinear amplifier to which the signal x of equation (1) is applied, the output signal y takes the following form: EQU y(t)=C(A).cos(2.pi..f.sub.0.t-.PHI.(A)+.phi.(t)) (5)
where C(A) is the amplitude of the output signal y, PA1 and .PHI.(A) is the phase shift of the output signal y, PA1 1. A curve C(A) wherein the amplitude C of the output signal y is a function of the amplitude A of the input signal, illustrated for example by the curve AM/AM, in an unbroken line, of FIG. 6A (amplitude/amplitude conversion curve); PA1 2. A curve .PHI.(A) wherein the phase shift .PHI. of the output signal y with respect to the input signal x is a function of the amplitude A of the signal x, called an amplitude/phase conversion curve, abbreviated as AM/PM, an example of which is shown in an unbroken line in FIG. 6B. PA1 1. The carriers, with respective frequencies f.sub.-1 and f.sub.1, and amplitudes C.sub.-1 and C.sub.1 at output; and PA1 2. The third-order intermodulation components, with respective frequencies f.sub.-3, f.sub.3, and amplitudes C.sub.-3, C.sub.3 at output.
which depends on the amplitude A(t) of the input signal x.
Thus, at a given instant t, the amplitude C(A) and the phase shift .PHI.(A) of the output signal y depend solely on the amplitude A of the input signal x at this instant t. It is thus possible to overlook the amplitude variations A(t) as a function of time and consider that the amplitude A is almost constant as can be seen in FIG. 3.
It is also useful to write in a complex form the envelopes of the signals x and y expressed here above, namely as the envelopes X and Y which take the following respective forms: EQU X=A.exp(j..phi.) (3)
(the envelope A considered as being constant in time) EQU Y=C(A).exp(j..phi.-.PHI.(A)) (6)
The response of a quasi-memoryless nonlinear amplifier can therefore be modeled and simulated simply on the basis of knowledge of the following two characteristic curves:
It can be shown that, similarly, the curve C(A) is the norm of the complex Chebyshev transform of the response characteristic y(x), the curve .PHI.(A) being the argument of the complex transform.
The complex envelope Y of the output signal can also be written in the form of two parts, namely a real part and an imaginary part, corresponding to an in-phase component P and a quadrature component Q, these components P and Q having the following forms: EQU P(A)=C(A).cos(.PHI.(A)) (7') EQU Q(A)=C(A).sin(.PHI.(A)) (7")
FIG. 7 shows an example of curves P(A) and Q(A) equivalent to the curves C(A) and .PHI.(A) of FIGS. 6A and 6B.
The known models of simulation of the response of quasi-memoryless amplifiers generally prefer to use characteristics in the form of pairs of curves P(A) and Q(A) rather than in the form of pairs of curves C(A) and .PHI.(A), although these pairs of curves are strictly equivalent.
According to a known principle of the simulation of nonlinear amplifiers, the amplifier that is made is precharacterized on the test bench. The precharacterizing is done with a signal having a specified frequency and amplitude in order to then simulate the response to a signal of any frequency and amplitude.
As shown schematically in FIG. 5, a signal with a single-frequency f.sub.0 taking different amplitudes A', A", A'" is applied to the amplifier tested to obtain its characteristics, illustrated for example in FIG. 6 or 7.
However, for amplifiers having a certain quantity of memory, it is observed that the characteristics vary to a major degree depending on the frequency f.sub.0.sup.-, f.sub.0 or f.sub.0.sup.+ of the signal to be amplified.
A known system for the simulation of such amplifiers has been explained by H. B. Poza in an article entitled "A Wideband Data Link Computer Simulation Model", in the "NAECON'75 Record", page 71. The article proposes plotting of several pairs of curves AM/AM and AM/PM for several frequencies f.sub.0.sup.-, f.sub.0 or f.sub.0.sup.+ of operation of the amplifier. FIGS. 6A and 6B thus show an example of three pairs of curves AM/AM and AM/PM obtained respectively at three frequencies f.sub.0.sup.-, f.sub.0 and f.sub.0.sup.+ located in the useful band BU of a directional radio link amplifier.
H. B. Poza's simulator stores only one pair of curves AM/AM and AM/PM, for example the pair of curves obtained at the frequency f.sub.0, and reconstitutes the other pairs of curves (not stored) corresponding to the other frequencies f.sub.0.sup.-, f.sub.0.sup.+ or to intermediate frequencies. A non-stored curve is deduced simply by translating the stored curve by an appropriate vector. The simulator computes the components along the axis (A) and along the axis (C) or (.phi.) of the translation vector to bring the curve for the frequency f.sub.0 ; shown in an unbroken line in FIG. 6A or 6B, as close as possible to the frequencies f.sub.0.sup.- or f.sub.0.sup.+, shown in dashed lines.
A simulation system of this kind gives too much of an approximation to simulate the distortions that appear on a quasi-memoryless amplifier at different frequencies.
Another drawback of a system of this kind is that it cannot be used to simulate the response of an amplifier with memory.
FIG. 9 illustrates another known system of simulation according to the model of A. A. M. Saleh, described in an article "Frequency-Independent and Frequency-Dependent Models of TWTA Amplifiers" November 1982, in "IEEE Transactions on Communication", Volume Com-29, No. 11, page 1715. The computation of the response to an input signal x of a quasi-memoryless nonlinear amplifier can be subdivided into two steps P(A,f) and Q(A,f) for the computation of two respective components yp and yq of the output signal y. The component yp is in phase with the input signal x while the component yq is in quadrature.
Saleh's stimulation system uses results for the characterization of the amplifier at several frequencies f, several pairs of curves P(A) and Q(A) being plotted at several frequencies f to compute transfer functions P(A,F) and Q(A,f) corresponding to each arm for the computation of the components yp and yq of the output signal y. Each of the transfer functions P(A,f) or Q(A,f) corresponds to the computation of a nonlinear response without memory effect, since no phase shift is introduced into each of these computation branches.
A. A. M. Saleh's article points out that the model can be applied to the amplification of single-frequency signals and, by conjecture, assumes that it will be applicable to the simulation of signals of any form.
Another drawback of this model is that it cannot be applied to amplifiers with memory, as the system does not realize distortions appearing at different frequencies when the amplitude of the signal varies at high speed with respect to the memorizing time constants.
For nonlinear amplifiers with memory ANLAM, the memorizing effects are greater, as the memorizing time is not negligible in comparison with the time of variation of the amplitude A(t). In such cases, a more complex method such as that of nonlinear differential equations or the development of the characteristic curves in sequences of functions is necessary to simulate the response of the amplifier with memory ANLAM.
An improved known model is proposed by M. T. Abuelma'atti in an article entitled "Frequency-Dependent Nonlinear Quadrature Model for TWT Amplifiers", in August 1984, in the journal IEEE Transactions on Communication, Volume Com. 32, No. 8, page 982. The modeling uses a development of the characteristic curves of a nonlinear amplifier in sequences of Bessel functions making it possible to simulate the response of amplifiers with memory.
FIG. 10 illustrates the simulation system described by M. T. Abuelma'atti which, as here above, comprises two branches of computations of the in phase component yp and the quadrature component yq of the output signal y, each arm computing the contribution of a sequence of N Bessel functions J1 depending on the amplitude A of the input signal x, in weighing each function J1 by a coefficient .alpha. and a factor G(f) of correction in frequency. The coefficients .alpha..sub.n and the factors G.sub.n (f) are computed after having established several pairs of curves P(A) and Q(A) that are characteristic of the nonlinear amplifier, the curves being plotted at several testing frequencies f of the amplifier.
With FIG. 8, it can be seen that two weighted sums of N Bessel functions of the first kind of first order, referenced J1(n.pi.A/D), enable the very precise interpolation of the curves P(A) and Q(A), like those of FIG. 7, by adjusting the weighting coefficients .alpha..sub.np and .alpha..sub.nq of these functions J1.
It can be noted that the Bessel functions are the Chebyshev transforms of sine functions and that the development, in sequences of Bessel functions, of the curves P(A) and Q(A) corresponds to a Fourier development, in sequences of sine functions, of the curves y(x) of nonlinearity of the amplifier, which is elegantly suited to the sinusoidal form of the hysteresis curves y(x) as shown in FIG. 2.
Theoretically, a system of this kind should enable the simulation of the amplification of multicarrier signals, namely signals comprising several sinusoidal components of distinct frequencies.
However, the nonlinear amplification of a multicarrier input signal is complicated by the appearance of distortions known as intermodulation phenomena. When a nonlinear amplifier receives several carrier frequencies at input, there are obtained at output, in addition to the amplified carriers, undesired harmonics known as intermodulation products, each harmonic having a frequency distinct from the frequencies of the carriers.
FIGS. 11-14 illustrate the appearance of the intermodulation phenomenon during the nonlinear amplification of a two-carrier signal.
FIG. 11 is a graph pertaining to the frequency of a two-carrier input signal x representing, for example, two carrier components with respective frequencies f.sub.-1 and f.sub.1 having an equal input amplitude A. The two carrier frequencies f.sub.-1 and f.sub.1, located in the useful frequency band BU of the amplifier are separated by a frequency difference df.
FIG. 14 is a graph pertaining to the frequency of an output signal y that corresponds to the amplification ANLAM with memory effect of the two-carrier input signal x of FIG. 11. It can be seen that the output signal y has a series of harmonics of various frequencies f and different amplitudes C.
The frequency of each of these intermodulation components is an integer combination of the carrier frequencies at input.
The detail of the output harmonics included in the useful band BU, illustrated in FIG. 14, is as follows:
FIG. 15 reproduces results according to Abuelma'atti's model which has enabled an estimation of the amplitudes C.sub.-1, C.sub.1, and C.sub.-3, C.sub.3 of carrier components and third-order intermodulation components.
However, the estimation of the amplitude of the intermodulation components by Abuelma'atti's model corresponds poorly to the reality of the measurements of intermodulation distortions on nonlinear amplifiers in multicarrier operation with high efficiency.
Indeed, a general phenomenon known as an envelope memory effect arises when a multicarrier signal is amplified. For this type of signal, the envelope, which is defined by the positive and negative limits in amplitude of the signal, is not constant.
In this case, it can no longer be assumed that the envelope is constant as in the quasi-memoryless models. In fact, the memorizing time constants are no longer negligible with respect to the time of variation of the envelope.
FIG. 12, which illustrates the temporal progress of the two-carrier input signal x of FIG. 11 shows, for example, that the envelope X(t) and -X(t) of the two-carrier signal varies very swiftly and in major proportions whereas the amplitude A of each carrier f.sub.1 and f.sub.-1 is assumed to be constant.
FIG. 13 which illustrates the temporal progress of the output signal y corresponding to the preceding two-carrier input signal x, shows that the envelope Y(t) and -Y(t) of the output signal y is deformed by the intermodulation distortions. The appellation `envelope memory effect` is used to designate such deformations of amplitude of the signal by a nonlinear amplifier with memory.
The known models do not take into account the two effects illustrated in FIGS. 16 and 17. In particular, FIG. 16 illustrates that the ratio C1/C3 (comparing the amplitude C1 of carriers with respect to the amplitude C3 of the intermodulation components) varies considerably depending on the frequency difference df of the carriers and depending on the precise value of the amplitude A of the carriers of the input signal.
Through the application of Abuelma'atti's model, the ratio C1/C3 does not depend on the frequency difference and varies continuously according to the input amplitude A.
The second observed effect is that the presence of a second carrier influences the output amplitude of the first carrier.
FIG. 17 shows, for example; output amplitude attenuation or resonance peaks C1 or C-1 of each of the carriers with frequencies f.sub.1 or f.sub.-1, depending on the frequency difference df between the two carriers (df being equal to f.sub.1 -f.sub.-1).
Therefore, the above-identified prior art models do not account for these effects. Moreover, in general, these models simply do not simulate any envelope memory effect.